Mixed-mode Fracture Toughness Research Articles

Analysis of Mixed-Mode I/II/III Fracture Toughness Based on a Three-Point Bending Sandstone Specimen with an Inclined Crack

The crack-propagation form may appear as an arbitrary mixed-mode fracture in an engineering structure due to an irregular internal crack. It is of great significance to research the mixed-mode fracture of materials with cracks. The coupling effect of multiple variables (crack height ratio, horizontal deflection angle and vertical deflection angle) on fracture parameters such as the stress intensity factors and the T-stress are the key points in this paper. A three-point bending specimen with an inclined crack was proposed and used to conduct mixed-mode fracture research. The fracture parameters were obtained by finite element analysis, and the computed results showed that the pure mode I fracture and mixed-mode fractures (mode I/II, mode I/III and mode I/II/III) can be realized by changing the deflection angles of the crack. The pure mode I and the mixed-mode fracture toughness of sandstone were obtained by a series of mixed-mode fracture experiments. The experimental results were analyzed with the generalized maximum tangential strain energy density factor criterion considering T-stress. The results showed that the non-singular term T-stress in the fracture parameters cannot be ignored in any mixed-mode fracture research, and the generalized maximum tangential strain energy density factor criterion considering T-stress can better predict the mixed-mode fracture toughness than other criteria.

Development of a mixed mode double cantilever beam specimen for the fracture characterization of adhesives under high displacement rate

In this paper, a new specimen called mixed mode double cantilever beam (MMDCB) was developed for the mixed mode fracture characterization of adhesives under high displacement rates. The MMDCB specimen was designed using finite elements simulations in order to determine the fracture toughness for a mode mixity in the plane I+II+III. Firstly, results from MMDCB specimens tested under quasi-static loading were experimentally compared to a reference single leg bending test. The test results, obtained with the two different specimens, exhibit consistent evaluations of the mixed mode fracture toughness. Secondly, the MMDCB specimen testing under asymmetric high displacement rate was validated through explicit simulations. The corrected beam theory with effective crack length was extended to the analysis of MMDCB specimens tested under high displacement rate. It was numerically proved to accurately determine the mixed mode fracture toughness under a displacement rate up to 1 m/s.

Fracture behaviour of hybrid fibre-reinforced roller-compacted concrete used in pavements

The aim of the present paper is to investigate the fracture properties of hybrid fibre-reinforced Roller-Compacted Concretes (RCCs), typically used in pavements. More precisely, tests to determine fracture toughness are performed, including both single and hybrid fibre-reinforced concrete specimens. Plain concrete specimens are also tested for comparison with the previous ones. The Modified Two Parameter Model, formulated by some of the present authors, is employed in order to compute the mixed-mode fracture toughness. Moreover, the ductility is evaluated through a toughness index, and the effect of the reinforcing fibres on the material post-peak behaviour is discussed.

Understanding the fracture mechanism of ring Brazilian disc specimens by the phase field method

Ring Brazilian disc specimens are favored for determining the tensile strength and mixed mode fracture toughness. To further understand the fracture mechanism of ring Brazilian disc specimens, the phase field method is used to investigate the cracking process and peak load of ring Brazilian disc specimens. First, the numerical validity and accuracy of the phase field method is verified by a benchmark example. Then, the effect of aperture ratio and crack inclination angle on the failure process and peak load of ring Brazilian disc specimens is studied. Finally, by combining the phase field method and J-integral method, the influence of prefabricated crack inclination angle and aperture ratios on mode I and II fracture toughness of cracked ring Brazilian disc specimens is discussed.

Interfacial mixed-mode fracture toughness characterization of flexible layered materials

Flexible hybrid electronics (FHEs) are finding increasing applications because they overcome many of the limitations of non-deformable traditional electronic boards while still maintaining low-cost fabrication. A critical key to the performance of FHEs depends on the adhesion energy of the interface between printed conductive silver pastes and a flexible substrate. Predicting the fracture energy and evaluating the reliability of these devices under large deformation is crucial in future design efforts. However, because of the size of the components and complex nonlinear behavior of the materials, standard methods of interface characterization may not always be practical. In this study, a new interface characterization experiment for FHE interfaces was created with the help of numerical models. The mixed-mode characterization experiment was performed using a bi-axial loading configuration where the bi-axial loading ratio was used to control the phase angle of the mode mixture. The loading ratio was chosen to produce mode II-dominant loading to better represent typical loading in application. The crack growth was measured using digital image correlation (DIC) by tracking displacement rate changes. Finally, the fracture energy of the interface was calculated based on the experimental data and using finite element (FE) model to include the effects of material inelasticity plasticity in the entire structure.

Fracture toughness analysis of HCCD specimens of Longmaxi shale subjected to mixed mode I-II loading

Longmaxi shale exhibits strong anisotropy due to its bedding planes induced by diagenesis. The anisotropic properties of shale have a significant effect on the stability control of geotechnical engineering. To investigate the influence of anisotropy of shale on its mixed mode fracture toughness, we performed Brazilian disc splitting tests on hollow center cracked disc shale specimens with different bedding and crack inclination angles (α and β, respectively). In this study, the fracture toughness of Longmaxi shale was calculated by the finite element method combined with either the J-integral or crack tip-opening displacement method. The results show that the dimensionless stress intensity factors and β values for pure mode-I and mode-II fractures both show anisotropic behavior by varying α. For all combinations of mode-I and mode-II loading, the fracture toughness also exhibits anisotropy by varying α; the mode-I fracture toughness decreases with increasing α when β > 30°, and the anisotropy is negligible for β = 0°. The anisotropy for mode-II fracture toughness is weak when β is small or large, whereas the anisotropy is significant when β = 45° and 60°. The effect of α on mode-I fracture toughness is greater than that on mode-II fracture toughness when β is small or large. Further, a comparison of four mixed-mode fracture criteria with the experimental results shows that the maximum tangential stress criterion for a transversely isotropic body can predict the mixed-mode fracture behavior of Longmaxi shale well. At the same time, it is suggested that the role of the T-stress should be considered to obtain more accurate prediction results.

Effects of cyclic freeze-thaw treatments on the fracture characteristics of sandstone under different fracture modes: Laboratory testing

For engineering projects in cold regions, the failure behaviour of jointed rocks is affected by freeze–thaw (F-T) cycle action. To reveal the fracture characteristics of rock under the influence of cyclic F-T treatments, fracture tests on semicircular specimens with different F-T cycle numbers were conducted. The fracture toughness values in different modes were investigated by SCB specimens with different crack inclinations (0°, 5°, 15°, 30°, 45° and 54°). The experimental results show that cyclic F-T treatments can lead to degradation in three kinds of fracture toughness values. Specifically, the value of KIC (fracture toughness in mode I) decreases by 3.1, 7.2, 15.0 and 24.3% after 20, 40, 60, and 80 F-T cycles, respectively. When the number of cycles increases from 20 to 80, the value of KIIC (fracture toughness in mode II) of the sandstone decreases by 8.43, 12.0, 18.8 and 27.9%. For the specimen with crack inclinations of β = 5°, 15°, 30° and 45°, after 80 F-T cycles, the Keff (effective fracture toughness) value decreases to approximately 83.7, 78.3, 79.1 and 76.7% of the initial value, respectively. The mixed-mode fracture toughness ratios Keff/KIC were calculated and compared with the theoretical solution. The experimental results of Keff/KIC agree well with the theoretical results calculated based on the MMTS criterion. Moreover, after F-T treatments, the fracture paths of the SCB specimens are more tortuous than those in specimens without F-T treatment. In addition, the fracture surface morphological characteristics of the SCB specimen were obtained by a 3D laser scanner. Overall, the fractal dimension value increases gradually with additional F-T cycles. This indicates that the F-T treatments lead to rough fracture paths and fracture surfaces.

Effect of polypropylene fibers on the mode I, mode II, and mixed-mode fracture toughness and crack propagation in fiber-reinforced concrete

Concrete is the most commonly used material in civil engineering and also the most conventional and cheap material available in the market. Concrete cracking and fracturing may cause irreparable damages to concrete structures. Hence, fiber-reinforced concretes have been introduced in recent years as a strategy to eliminate these drawbacks to a large extent. In this study, crack propagation and the fracture toughness of concrete specimens without polypropylene (PP) fibers and those containing 0.2, 0.35, and 0.5 vol% of PP fibers were investigated through testing the straight notched Brazilian disc specimens. Furthermore, crack propagation from the pre-existing cracks in the specimens was investigated, and the mode I, mode II, and mixed-mode I/II fracture toughness were also calculated. The Brazilian disc (BD) test was performed on the specimens at different inclination angles of 0, 15, 28.83, 60, 75, and 90° relative to the direction of pre-existing cracks. According to the experimental results, at angles less than 75° (0 < α less than 75), the wing cracks initiated from the tip of pre-existing cracks, and as the loading continues, the path of crack propagation and growth approaches the loading direction. At angles equal to or greater than 75°, the crack initiated with a distance d from the crack tip. This distance was larger in the fiber-free specimens than in the fiber-reinforced specimens. The results showed that the mode I, mode II, and mixed-mode I/II fracture toughness of the specimen containing 0.35 vol% of PP fibers were higher than the fracture toughness of the fiber-free specimens or those containing other PP fiber levels.

Mixed-mode fracture toughness testing of a Cu/Ag bimetallic interface via atomistic simulations

This work presents the evaluation of mixed-mode fracture toughness for an interface crack using molecular dynamics simulations. A Cu/Ag bimetallic structure with an interface crack was configured, where the atomic interactions were characterized based on the embedded-atom method potential. A bimaterial K-field of linear elastic fracture mechanics was employed as a remote loading for the mixed-mode failure. The traction ratio of the shear to normal component in front of a crack tip was defined as the mode mixity. The critical value of the J-integral for the onset of crack growth along the interface was measured as the interfacial fracture toughness; the value was also compared to the critical energy release rate and the Griffith fracture toughness. The interfacial fracture toughness of a Cu/Ag bimaterial was found to exhibit significant dependence on mode mixity for an interface crack, which resulted from various types of atomic-scale deformation at the interface.

Mixed-mode I + II tensile fracture analysis of thermally treated granite using straight-through notch Brazilian disc specimens

The destruction and fracture failure of heat-treated rock structures have been major issues in the underground engineering, such as disposal of highly radioactive nuclear waste, deep mining and exploitation of geothermal resources. Although several literatures have focused on studying the mode I fracture toughness and mode I fracture characteristics of heat-treated rocks, studies of the thermal effect on the mixed-mode fracture toughness and mixed-mode fracture characteristics are rare. Additionally, there is a lack of systematic study to analyse the fracture characteristics of heated rocks on theoretic aspects. In this paper, lots of mixed-mode I + II fracture tests were conducted on a heat-treated granite using straight-through notch Brazilian disc specimens. A total of six specimen groups (25, 100, 200, 400, 600 and 800 °C) and four loading mixities (Mode I loading, mode II loading and two mixed-mode loadings) are selected to apply the fracture tests. The results show that temperature treatment can both significantly affect the brittleness and the mixed-mode fracture toughness of the granite, but the fracture initiation angle is not sensitive to high temperature. The mode I fracture toughness and mixed-mode fracture toughness develop similar trend with increasing treatment temperature. The theoretical fracture models can be effectively applied to predict variations of the mixed-mode fracture parameters. This research also indicates that fracture parameters at high temperature are likely to be predicted by the well-known fracture criterion by only taking the rock physical and mechanical parameters at natural temperature. This work could provide a reference to the research on the mechanical properties and fracture failure of rocks during restoring of post-fire rock structures or hydraulic fracturing of hot dry rocks.

The effect of in-plane layer orientation on mixed-mode I-II fracture behavior of 3D-printed poly-carbonate specimens

Mechanical components produced by the 3D-printing technique contain small voids by nature, which make them susceptible to fracture. Therefore, understanding the fracture behavior of these components improves the applicability of this manufacturing method. In this study, the effect of layer orientation is investigated on the mixed-mode I/II fracture behavior of additively manufactured poly-carbonate produced using a fused deposition modelling (FDM) printer. A total of 48 semi-circular bend (SCB) specimens with different mode mixities and printing orientations are tested. The curves for the maximum tangential stress (MTS) and the generalized MTS (GMTS) criteria are then produced using the mode I fracture properties for the weakest and the strongest direction of the printed material. This results in two failure curves for each of the criteria. Comparing the mixed-mode fracture toughness data with these curves, it is observed that all the data are placed between the two GMTS curves (regarding error bands). As an engineering approach, the band created by the GMTS curves, called the GMTS range, is suggested as an acceptable band for use in engineering designs. Furthermore, in a more detailed analysis, the fracture paths of the specimens are correlated with the position of the experimental data in the GMTS range. Three different fracture modes occur during the tests depending on the layer orientation and mode mixity of the sample. The inter-layer and the cross-layer modes correspond to the data points on the lower and upper fracture curves, while the data points in the middle represent the samples undergoing the crack multi-kinking mode.

Mixed mode testing of a multi-directional woven laminate

Mixed-mode fracture toughness tests were carried out on a multi-directional laminate making use of a Brazilian disk specimen. The composite laminate consisted of plain, balanced woven plies with tows in the $$0^{\circ }/90^{\circ }$$ -directions and the $$+45^{\circ }/-45^{\circ }$$ -directions. The delamination was placed between two of these plies by means of a polytetrafluoroethylene (PTFE) film. Tests at various loading angles were performed in order to obtain a wide range of mode mixities. Each ply was homogenized by means of a micro-mechanical model to obtain its effective properties. The specimens were analyzed by means of the finite element method. An interaction energy or M-integral was extended for this interface to obtain the stress intensity factors. The latter were used to determine the critical interface energy release rate and two phase angles. Employing this information, a three-dimensional failure criterion proposed elsewhere was presented. The criterion may be used to predict failure of a composite structure containing a delamination along the interface and material studied here.

Mixed-mode fracture toughness of a structural adhesive by the single-leg bending test

To increase the confidence in the design of adhesive structures, it is important to be able to accurately predict their strength and fracture properties (e.g., critical strain energy release rate in tension, JIC, and shear, JIIC). Since in most cases the applied loads induce mixed-mode crack growth, it is highly relevant the perception of fracture under these conditions. This work presents an experimental study using the Single-Leg Bending (SLB) test on specimens bonded with Araldite® 2015, to study and compare the mixed-mode fracture properties. For this purpose, the J-integral method was applied to estimate the tensile (JI) and shear fracture energy (JII). Framing the obtained values in the fracture envelope enabled to select which power-law failure criterion is more appropriate for the Araldite® 2015. Moreover, the tensile and shear cohesive zone model (CZM) laws were obtained for the adhesive by the direct method. Overall, a very good agreement on the fracture properties was obtained between specimens. The CZM laws also showed a good correspondence between specimens, resulting in a novel methodology for integrated mixed-mode material characterization of structural adhesives for possible use to design adhesive joints.

Experimental determination of toughness under mode I/II loading

The mixed-mode fracture toughness of a 42CrMo4 high-strength steel under mode I/II loading was investigated. The steel was processed in a steel casting simulator where it was poured through a spaghetti-type filter into a ceramic crucible. The machined compact tension shear specimens were heat treated in order to obtain the quenched and tempered state. The designs of the specimen and the loading device enabled testing at different loading angles leading to different ratios KI/KII. Strain gauges were applied in order to analyze the stress field around the crack tip. It was observed that the strain gauges can be reasonably applied to measure KI. However, large errors occurred during the measurement of KII. The specimens fractured in a brittle manner. However, no valid plane-strain fracture toughness was obtained. With increased loading angles, mode I fracture toughness decreased while mode II fracture toughness increased. Furthermore, it was found that stretch zone was flattened with increased loading angle.

Effects of biocompatible Nanofillers on mixed-mode I and II fracture toughness of PMMA base dentures

A modified single edge cracked bend beam specimen called “inclined edge crack asymmetric bend” (IE-CAB) specimen was designed and proposed for investigating mixed mode I/II fracture toughness behavior of brittle materials. Using a large number of finite element analyses performed for different geometry and loading conditions, it was demonstrated that unlike the conventional single edge notch beam specimen, the IE-CAB configuration can provide full combinations of mode mixities from pure mode I to pure mode II. Then the IE-CAB specimen was employed for mixed mode I/II fracture toughness testing of two PMMA based denture materials (i.e. neat PMMA and toughened PMMA with Nano-hydroxyapatite (HAP)and Nano-alumina (Al2O3) particles). The obtained experimental results showed that adding bio-compatible (HAP and Al2O3) Nano-particles can increase both modes I and II fracture resistance (KIc and KIIc) values of base PMMA denture. However, the influence of such particles was more pronounced on enhancing mode I fracture toughness (KIc) value. Pure mode II fracture toughness value was obtained less than the pure mode I fracture toughness in the tested specimen showing the higher crack growth risk of such PMMA base dentures against dominantly shear loads. The well-known maximum tangential stress theory was also used for estimating the obtained experimental data both for mixed mode fracture toughness and fracture initiation direction in the tested PMMA base denture materials.

Two- and Three-Dimensional Failure Criteria for Laminate Composites

Abstract Several two- and three-dimensional mixed-mode interface failure criteria are proposed for predicting delamination failure in multidirectional, laminate composites. The proposed criteria, based on the stress intensity factors K1, K2, and KIII, as well as the critical interface energy release rate Gic and phase angles ψ and ϕ, are examined using results obtained from Brazilian disk mixed-mode fracture toughness tests. Two material systems are considered. The first contains a delamination along an interface between a unidirectional fabric and a plain woven fabric. The second is composed of a plain woven fabric with fibers oriented in different directions in succeeding plies. The former was manufactured by means of a wet-layup and the latter is a prepreg. Finally, a statistical analysis is carried out to obtain a failure curve or surface with a 10% probability of unexpected failure and a 95% confidence. These curves or surfaces may be used to predict failure of structures containing these laminates and to assist in composite design.

Adhesive thickness effects on the mixed-mode fracture toughness of bonded joints

ABSTRACTAiming to predict the strength of bonded joints by techniques such as cohesive zone models (CZM), it is highly relevant to estimate the adhesive strength and fracture toughness (GC). Here, the tensile and shear fracture toughness (GIC and GIIC, respectively) and the corresponding mixed-mode behaviour acquire special relevancy. However, it is known that these parameters are highly dependent on the adhesive thickness (tA). The present work experimentally addresses the tA effect on the mixed-mode behaviour of bonded joints, namely on the tensile and shear fracture energies (GI and GII, respectively), using the Single-Leg Bending (SLB) test. Different data reduction schemes were applied. With this purpose, the respective resistance curves (R-curves) were calculated, which enabled plotting the respective fracture envelope for a sample tA by the knowledge of the pure-mode GIC and GIIC. Overall, it was possible to obtain a good agreement between methods for the mixed-mode GI and GII calculation and to estimate the most suitable fracture envelope of the adhesive for a given tA. The compliance-based beam method (CBBM) was found to be particularly suited to perform data reduction, since it accounts for the adhesives’ ductility and it is not affected by crack length (a) measuring errors.

T-strain effects in kinked interfacial fracture of bonded composites

Strain-based criteria are employed to predict fracture initiation behavior in bi-material cracked components. Two versions of the maximum tangential strain criterion are developed theoretically for the case of a crack existing at the interface of two dissimilar isotropic elastic solids to predict kinking angle and the mixed-mode interfacial fracture toughness. The first version (MTSN) is developed based on the singular strain fields while the second version (EMTSN) takes into account the effects of the first non-singular strain term (T-strain) as well as the singular terms. The theoretical effect of T-strain on the calculation of the kinking angle and the mixed-mode interfacial fracture toughness is studied. Then, both MTSN and EMTSN criteria are examined by comparing theoretical predictions to the previously reported experimental results for the kinking angle and mixed-mode interfacial fracture toughness in different bonded composite specimens. It is found that considering T-strain can significantly improve the theoretical predictions of the experimental results provided by the maximum tangential strain criterion.

Mixed-mode fracture toughness versus thickness and yield strength in aluminum alloys

Variations in in-plane mixed-mode fracture toughness versus changes in thickness of shear CT (CTS) specimens and loading direction and effects of yield strength of different aluminum alloys have been investigated by experimental testing and numerical analysis. Several samples were made by Al2024-O, Al6061-T6 and Al7075-T6 alloys. Based on the results, increasing the thickness reduces the mixed-mode fracture toughness and near to the critical thickness, this reduction is lesser. Increase in mixed-mode loading angle for brittle materials has not significant effects on the toughness while in softer materials by changing the angle from 15° to 60°, the amount is halved. Near the mode I fracture conditions, there is no meaningful relationship between the yield strength and fracture toughness but with an increase in the second mode effects, these parameters will be proportional. The mixed-mode toughness of the alloys with different thicknesses can be calculated numerically with a precise accuracy by applying failure load in the analysis.

Evaluation of the mixed mode (I/II) fracture toughness of cement emulsified asphalt mortar (CRTS-II) using mixture design of experiments

Cement emulsified asphalt mortar (CEAM) is a key component of ballastless rail track systems which is tasked with damping the train movement energy and transferring loads to the concrete roadbed. This mortar consists of asphalt emulsion, sand, cement, and water and enjoys better toughness and flexibility properties than cement mortar thanks to the combined effect of cement and asphalt emulsion. One of the primary causes of failure in this mortar is cracking at low temperatures. This study investigated the fracture toughness of CEAM (CRTS- II) with different volume percentages of mortar constituents, namely cement, sand, water, and asphalt emulsion, at low temperature in the linear elastic fracture mechanics (LEFM) framework. The critical stress intensity factors of the mortar for pure tensile (mode I), pure shear (mode II), and mixed tensile-shear (mixed mode I/II) fractures with Me values of respectively 1.0, 0, and 0. 67 were obtained. Considering the necessity of examining the effect of mix design ratios and their interactions and the need to limit these ratios to ensure acceptable rheological and mechanical properties, the experiments were designed using the D-Optimal mixture design method at 5% significance level. By assuming a quadratic model between the critical stress intensity factors of each fracture mode and the volume percentages of mortar constituents, a total of 20 randomized mix designs were obtained. For each mix design, the semi-circular bending (SCB) test was performed with at least 3 replications. The regression models based on the experimental results were developed. The findings demonstrated the dependence of mode I, mode II, and mixed mode I/II critical stress intensity factors on the mix design ratios. The lowest and highest fracture toughness estimates were related to the mixed tensile-shear and pure shear modes, respectively. Finally, the mixture design method was used to delimit the optimum mix design region for maximizing the fracture toughness of all three modes.